What's the Next Step in Advanced Algebra After Artin and Dummit?

[samspotting]

I just finished a very rigorous second course in linear algebra covering determinants, diagonalization, cayley hamilton thm and invariant subspaces, normal/self adjoint/unitary operators and the spectral thm, and jordan forms. I also have finished calc 3, analysis in several dimensions.

I flipped through artin and saw that it covered a lot of what I knew already (just from looking at the table of contents). What is a good book for someone with my background? I've heard bad things about dummit and foote.

 

[Landau]

Personally, I like D&F. If it's too easy (it's about the same level as Artin), you can go right to Hungerford.
So you have a good background in linear algebra...but have you seen anything on group and ring theory?

 

[samspotting]

I have never studied abstract algebra, so I know very little of even what it covers. I know the basic definition of a ring and group. I was confused as to why there is so much lin alg in artin. Is it from a group theory perspective?

 

[Vid]

Artin is an excellent book. Just skip or skim over chapters 1,3,4 and do the rest of the book normally. The books set up the way it is because the course at MIT the book is based contained abstract algebra and abstract linear algebra together.

Or Robert Ash's book is free and assumes linear algebra, although his book is meant for a first year graduate class instead of an undergrad class.
http://www.math.uiuc.edu/~r-ash/Algebra.html